Which of the following is an equivalent expression to 14−79−13 with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point)
Responses
1913 ⋅14−7
913147
147913
14−7⋅913
The equivalent expression with only positive exponents would be 1913 ⋅14−7.
To simplify the expression 14−79−13 using the Property of Negative Integer Exponents, we need to flip the base and change the sign of the exponent.
First, let's flip the base:
14-7 = 1/147
Now, let's change the sign of the exponent:
(1/147)-13
So, the equivalent expression with only positive exponents is 1913 ⋅14−7.
Therefore, the correct answer is: 1913 ⋅14−7.
To find an equivalent expression to 14−79−13 with only positive exponents, we can apply the Property of Negative Integer Exponents.
The Property of Negative Integer Exponents states that any term with a negative exponent can be transformed into its reciprocal by changing the sign of the exponent.
So, let's apply this property:
14−79−13 = (1/14^7) ⋅ 9^13
Now, let's simplify further:
= (1/(14^7)) ⋅ (3^2 ⋅ 3^11)
To simplify more, we'll combine the exponents of the same base:
= (1/(14^7)) ⋅ 3^13
Therefore, the equivalent expression with only positive exponents is 3^13 / 14^7, which can be written as option (A) 1913 ⋅ 14^(-7).